Kansas Standard 1: Number & Computation The student uses numerical and computational concepts and procedures in a variety of situations.

Benchmark 1: Number Sense – The student demonstrates number sense for whole numbers, fractions, and money using concrete objects in a variety of situations.

Benchmark 2: Number Systems and Their Properties – The student demonstrates an understanding of whole numbers with a special emphasis on place value.

Indicator #

Skill Area:

Indicator Language

Knowledge Indicator:

MHS12K3a

MHS12K3a

MHS12K3a

1b Recall or recognize mathematics terms, definitions, or concepts

3.   names, uses, and describes these properties with the real number system

and demonstrates their meaning including the use of concrete objects:

a.          commutative (a + b = b + a and ab = ba), associative [a = (b + c) = (a + b) + c and a(bc) = (ab)c], distributive [a (b + c) = ab + ac], and substitution properties (if a = 2, then 3a = 3 x 2 = 6);

   2b Do computational procedures or algorithms

3a Communicate mathematical ideas or rules and/or explain the process

MHS12K3b

   2b Do computational procedures or algorithms

2. identity properties for addition and multiplication and inverse properties of addition and multiplication (additive identity: a + 0 = a, multiplicative identity: a • 1 = a, additive inverse: ⁺5 + ^-5 = 0, multiplicative inverse: 8 x 1/8 = 1);

MHS12K3c

1b Recall or recognize mathematics terms, definitions, or concepts

c.        symmetric property of equality (if a = b, then b = a);

MHS12K3e

2b Do computational procedures or algorithms

e.  zero product property (if ab = 0, then a = 0 and/or b = 0).

Benchmark 3: Estimation – The student uses computational estimation with whole numbers in a variety of situations.

MHS13A1

MHS13A1

MHS13A1

3c Explain findings and/or results from data analysis strategies

1.         adjusts original rational number estimate of a real-world problem based on additional information (a frame of reference) $, e.g., estimate how long it takes to walk from here to there; time how long it takes to take five steps and adjust your estimate.

  4f Identify faulty arguments or identify misrepresentations of data

5b Apply mathematics in contexts outside of mathematics (whenever possible, include diagrams/visuals.)

Benchmark 4: Computation – The student models, performs, and explains computation with whole numbers using concrete objects in a variety of situations.

MHS14A1a

5b Apply mathematics in contexts outside of mathematics (whenever possible, include diagrams/visuals.)

1.        generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with:

a.         applications from business, chemistry, and physics that involve addition, subtraction, multiplication, division, squares, and square roots when the formulae are given as part of the problem and variables are defined (2.4.A1a) $, e.g., Given F = ma, where   F = force in newtons, m = mass in kilograms, a = acceleration in meters per second squared.  Find the acceleration if a force of 20 newtons is applied to a mass of 3 kilograms;

MHS14A1b

5b Apply mathematics in contexts outside of mathematics (whenever possible, include diagrams/visuals.)

b.         volume and surface area given the measurement formulas (2.4.A1f);

MHS14A1d

5b Apply mathematics in contexts outside of mathematics (whenever possible, include diagrams/visuals.)

d.     application of percents (2.4.A1a) $, e.g., compound interest given the formula; 

Standard 2: Algebra – The student uses algebraic concepts and procedures in a variety of situations.

Benchmark 1: Patterns – The student recognizes, describes, extends, develops, and explains relationships in patterns using concrete objects in a variety of situations.

Benchmark 2: Variables, Equations, and Inequalities – The student solves addition equations using concrete objects in a variety of situations.

MHS22A2a

MHS22A2a

MHS22A2a

2d Solve equations, formulas, or routine word problems

2.  represents and/or solves real-world problems with (2.4.A1a-c):

a.        N linear equations and inequalities both analytically and graphically $, e.g., ex;

3b Use representations to model mathematical ideas

  5b Apply mathematics in contexts outside of mathematics (whenever possible, include diagrams/visuals.)

MHS22K3c

MHS22K3c

1b Recall or recognize mathematics terms, definitions, or concepts

3.  solves (2.4.K1g):

      c.   systems of linear equations with two unknowns using integer coefficients and constants;

  2d Solve equations, formulas, or routine word problems

 Benchmark 3: Functions – The student recognizes and describes whole number relationships using concrete objects in a variety of situations.

MHS23A2

MHS23A2

3e Show and/or explain relationships between models, diagrams, and/or other representations

2.   interprets the meaning of the x- and y- intercepts, slope, and/or points on

     and off the line on a graph in the context of a real-world situation (2.4.A1e),

     e.g., The graph below represents a tank full of water being emptied.  What

     does the y-intercept represent?  What does the x-intercept represent?  What is

     the rate at which it is emptying?  What does the point (2, 25) represent in this

     situation?  What does the point (2,30) represent in this situation?

5b Apply mathematics in contexts outside of mathematics (whenever possible, include diagrams/visuals.)

MHS23K6

3e Show and/or explain relationships between models, diagrams, and/or other representations

6.         recognizes how changes in the constant and/or slope within a linear function changes the appearance of a graph (2.4.K1f.

Benchmark 4: Models – The student uses mathematical models including concrete objects to represent, show, and communicate mathematical relationships in a variety of situations.

Geometry – The student uses geometric concepts and procedures in a variety of situations.

Benchmark 1: Geometric Figures and Their Properties – The student recognizes geometric shapes and their attributes using concrete objects in a variety of situations.

Application

Indicator:

MHS31A1b

5b Apply mathematics in contexts outside of mathematics (whenever possible, include diagrams/visuals.)

1.        solves real-world problems by (2.4.A1a,f):

b.   applying the Pythagorean Theorem, e.g., when checking for square corners on concrete forms for a foundation, determine if a right angle is formed by using the Pythagorean Theorem;

Benchmark 2: Measurement and Estimation – The student estimates and measures using standard and nonstandard units of measure with concrete objects in a variety of situations.

Benchmark 3: Transformational Geometry – The student develops the foundation for spatial sense using concrete objects in a variety of situations.

Application

Indicator:

MHS33A1

MHS33A1

MHS33A1

3e Communicate mathematical ideas or rules and/or explain the process

1.         analyzes the impact of transformations on the perimeter and area of circles, rectangles, and triangles and volume of rectangular prisms and cylinders (2.4.A1f), e.g., reducing by a factor of ½ multiplies an area by a factor of ¼ and multiplies the volume by a factor of 1/8, whereas, rotating a geometric figure does not change perimeter or area.

4a Determine the truth of a mathematical pattern, a mathematical statement, and/or proposition or make predictions

  5b Apply mathematics in contexts outside of mathematics (whenever possible, include diagrams/visuals.)

Benchmark 4: Geometry From An Algebraic Perspective – The student identifies one or more points on a number line in a variety of situations.

MHS34K4

MHS34K4

2b Do computational procedures or algorithms

4.   finds and explains the relationship between the slopes of parallel and

    perpendicular lines (2.4.K1f).

  3d Develop and/or explain relationships between concepts

MHS34K6

MHS34K6

MHS34K6

1b Recall or recognize mathematics terms, definitions, or concepts

6.   recognizes the equation of a line and transforms the equation into slope-

    intercept form in order to identify the slope and y-intercept and uses this

    information to graph the line (2.4.K1f).

  2b Do computational procedures or algorithms

  3a Communicate mathematical ideas or rules and/or explain the process

Standard 4: Data – The student uses concepts and procedures of data analysis in a variety of situations.

Benchmark 1: Probability – The student applies the concepts of probability using concrete objects in a variety of situations.

MHS41K3

MHS41K3

1b Recall or recognize mathematics terms, definitions, or concepts

1.          explains the relationship between probability and odds and computes one given the other (2.4.K1a,k).

  2b Do computational procedures or algorithms

Benchmark 2: Statistics – The student collects, records, and explains numerical (whole numbers) and non-numerical data sets including the use of concrete objects in a variety of situations.

MHS42A1a

MHS42A1b,

MHS42A1c,

MHS42A1d,

MHS42A1e,

MHS42A1f,

MHS42A1g,

MHS42A1h

5c Analyze data or recognize patterns

1.          uses data analysis (mean, median, mode, range, quartile,  interquartile range) in real-world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays (2.4.A1i) $:

1. frequency tables;
2. bar, line, and circle graphs;
3. Venn diagrams or other pictorial displays;
4. charts and tables;
5. stem-and-leaf plots (single and double);
6. scatter plots
7. box-and-whiskers plots;
8. histograms.

MHS42K4

3c Explain findings and/or results from data analysis strategies

1.         explains the effects of outliers on the measures of central tendency (mean, median, mode) and range and interquartile range of a real number data set (2.4.K1a).

MHS42K5

MHS42K5

MHS42K5

1b Recall or recognize mathematics terms, definitions, or concepts

5.  approximates a line of best fit given a scatter plot and makes predictions using the equation of that line (2.4.K1d,l).

3e Show and/or explain relationships between models, diagrams, and/or other representations

  5c Analyze data or recognize patterns